Trouton–Noble Paradox

The 1903 Trouton–Noble experiment found no rotation of a suspended charged capacitor from motion through a proposed ether. This tool compares the same ideal vacuum capacitor in its rest frame S′ and a laboratory frame S, where it moves along x at βc. All geometry and voltage inputs refer to S′. θ₀ is the angle of the line between plate centers to x, not the angle of a plate surface.

Edit the values to compare both frames immediately. The two drawings use the same geometric scale and show Lorentz contraction along x. Plate width and gap are schematic; force and acceleration arrows are normalized separately. There is no artificial oscillation or time simulation. Purple F is the electromagnetic force on the negative plate due to the other plate. Dashed green a is its initial acceleration if released. A held capacitor remains stationary in S′; the supporting forces are not drawn.

U₀ = ε₀A₀V₀²/(2d₀), F₀ = U₀/d₀. In S, r = (d₀cosθ₀/γ, d₀sinθ₀) and F = (−F₀cosθ₀, −F₀sinθ₀/γ). The torque of the force pair about its center is τz = U₀β²sinθ₀cosθ₀. It can be nonzero. However F = dp/dt is not ma: ax = Fx/(m₀γ³), ay = Fy/(m₀γ). The acceleration is parallel to −r, hence no initial turning tendency. No guessed opposite torque is inserted.

Details show fields, initial acceleration for the chosen mass per plate, and actual electromagnetic field momentum ∫ε₀(E×B)dV. This is not a “hidden momentum” estimate. The lab field energy and momentum exclude mechanical support energy and stress. Ideal thin parallel plates, uniform fields, negligible fringing, no dielectric, gravity, finite collapse or torsion-fiber dynamics. Large gap-to-width ratios trigger an approximation warning. ε₀ uses the CODATA 2022 central value; calculations stay in your browser.

Franklin: The lack of rotation in the Trouton–Noble experiment (2006) · CODATA 2022

Changes update both views immediately. Use the beta and angle sliders to explore directions; exact text fields retain precision. Reset restores all defaults. Options contains examples, voltage, area, gap and mass per plate. Only raw input text is stored, including partial or invalid entries; no computed fields, diagrams or menus are saved.